This document studies domain decomposition techniques for the solution of partial differential equations on a domain divided into several subdomains. These techniques have special applications in the solution of elliptic problems on irregular domains and parallel computation. A unifying feature of these techniques is the use of preconditioned conjugate gradient method in solving for the unknowns on the interfaces of the subdomains, or in some cases, on the whole domain. Since each iteration involves solving problems on each subdomain, it is essential to keep the number of iterations low. For this reason, much effort has been devoted recently to the construction of good preconditioners for the conjugate gradient methods. This paper surveys the most common preconditioners that have appeared in the literature, including a new class that we have developed recently. One objective is to illuminate the relationships among these preconditioners. (Author)

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